Even the most cursory reader of Husserl’s writings must be struck by the frequent references to essences (“Wesen”, “Essenzen”), Ideas (“Idee”), kinds, natures, types and species and to necessities, possibilities, impossi- bilities, necessary possibilities, essential necessities and essential laws. What does Husserl have in mind in talking of essences and modalities? What did he take the relation between essentiality and modality to be? In the absence of answers to these questions it is not clear that a reader of Husserl can (...) be said to understand him. (shrink)

It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having other functions as value. (...) Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and “value-ranges”. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the lambda calculus. (shrink)

In the present paper, we discuss Husserl's deep account of the notions of ?calculation? and of arithmetical ?operation? which is found in the final chapter of the Philosophy of Arithmetic, arguing that Husserl is as far as we know the first scholar to reflect seriously on and to investigate the problem of circumscribing the totality of computable numerical operations. We pursue two complementary goals, namely: (i) to provide a formal reconstruction of Husserl's intuitions, and (ii) to demonstrate on the basis (...) of our reconstruction that the class of operations that Husserl has in mind turns out to be extensionally equivalent to the one that, in contemporary logic, is known as the class of partial recursive functions. (shrink)

Hintikka and Sandu had argued that 'Frege's failure to grasp the idea of the standard interpretation of higher-order logic turns his entire foundational project into a hopeless daydream' and that he is 'inextricably committed to a non-standard interpretation' of higher-order logic. We disagree.

The ideas of the German philosopher and mathematician Gottlob Frege lie at the root of the analytical movement in philosophy. Frege and Other Philosophers comprises all of Professor Dummett's published and previously unpublished essays on Frege, with the exception of those included in his Truth and Other Enigmas. In some of these essays he explores the relation of Frege's ideas to those of his predecessors and contemporaries. In others he considers critically some interpretations of Frege, and develops the argument for (...) a sound understanding of Frege's thought which he first delineated in The Interpretation of Frege's Philosophy. Several of the essays illustrate his contention that Frege's work remains the best starting point for the investigation of problems concerning truth, meaning, thought, and language, which are still among the most contentious issues in modern analytical philosophy. Any discussion of Frege's ideas is therefore also an exploration of fundamental and as yet unresolved issues of philosophy. (shrink)

Husserls »Logische Untersuchungen« sind eines der folgenreichsten Werke der neueren Philosophiegeschichte. Mit dem ersten Erscheinen in den Jahren 1900 und 1901 (Max Niemeyer Verlag, Halle/Saale) nimmt jene Schule ihren Anfang, deren Name im Untertitel des zweiten Bandes zum ersten Mal sinnfällig wird: die Phänomenologie. Husserl sah damals in diesem Werk »Versuche zur Neubegründung der reinen Logik und Erkenntnistheorie«, die den Grund zu einem größeren Gedankengebäude zu legen imstande waren. Sie wollten freilich kein bloßes Programm sein, sondern »Fundamentalarbeit an den unmittelbar (...) erschauten und ergriffenen Sachen« darstellen. Die weitere Arbeit an der Ausprägung der phänomenologischen Philosophie führte schon nach wenigen Jahren zu neuen Problemen, zu vertieften Erkenntnissen und zu schärferen Formulierungen. Ihnen trägt die zweite, zum Teil tiefgreifend umgearbeitete Auflage Rechnung, deren Text seither in unveränderter Form immer wieder nachgedruckt wurde. (shrink)

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.

"This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.

This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...

Against some very common views (e.g. Dummett), this paper argues that Frege did not have a standard interpretation of higher-order logic and for this reason his programme in the foundations of mathematics was a nonstarter.

The ideas of the German philosopher and mathematician Gottlob Frege lie at the root of the analytic movement in philosophy; Michael Dummett is his leading modern critical interpreter and one of today's most eminent philosophers. This volume collects together fifteen of Dummett's classic essays on Frege and related subjects.